curve name
probability density function (pdf)
-symbol f(x) to represent the curve
-helps find probability dist
cumulative dist function
(cdf)
-evaluates under the curve
-measured not counted
-whole area under curve=1
-no exact value, its a range between (c < x < d)
-P(x=c)=0, no width, no area
for CDF, the probability is equal to
area
uniform dist
-continuous (measured)
-equally likely (same chance)
-When solving problems, pay attention to whether the endpoints are included or not:
Inclusive: the endpoints count
Exclusive: the endpoints don’t count
-notation: X- U(a,b) where as is lowest and b is highest
go over example 9
graph shapes for uniform, normal, and exponential
uni- side bar
norm- bell curve
expo- down curve slope
normal dist
-continuous
-bell shaped, symmetrical, vertical line drawn at u
-two parameters: mean and SD
notation: X ~ N(μ, σ)
-change is mean or SD can cause the shape of curve to change and shift
normal dist: standard normal dist
-values called z scores
- z=x-u/sigma
-notation: X ~ N(μ, σ)
-Z-score = how many standard deviations x is above or below the mean.
x > mean → positive z right
x < mean → negative z left
x = mean → z = 0
Standard norm dist: x=μ+zσ
is used to find the actual value (x) on a normal distribution when you know:
μ = mean
σ = standard deviation
z = how many standard deviations away from the mean
empirical rule
Empirical Rule (68-95-99.7 rule):
~68% of values are within 1σ of the mean
~95% are within 2σ
~99.7% are within 3σ
Basically: almost everything is within 3 standard deviations of the mean.
to find probability on z score
turning p(x< X) into z number and find prob in chart
find percentile on z score
find the closest number to percentile within chart number, located z score
then use the fomula x=μ+zσ
when given two z score
-look at the empirical value amd sigma
-calculate with the sigma
-turn into z score
-subtract numbers
-should be the empirical %
